We have epitaxially grown ZnMgTe ternary alloys, whose Mg content is between 0% and 50%, on (100) GaAs substrates by metalorganic chemical vapor deposition. The band-gap energy estimated from the emission wavelength at room temperature can be varied from 2.26 to 2.57 eV. In the photoluminescence (PL) measurements at 4.2 K, band-edge emission was clearly observed up to Mg content of 25%. The refractive index decreases as Mg content increases. In the PL spectra of double heterostructures of ZnTe/ZnMgTe at 4.2 K, strong emission and quantum size effect were observed. These results suggest that effective carrier and optical confinement are possible.